How to find a partial derivative with respect to a matrix?

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Jan Korbel

have you tried http://en.wikipedia.org/wiki/Matrix_calculus? I think that your function CAX is nothing else than scalar, so you get matrix, because you differentiate w.r.t. each element of matrix

Robert Fraczkiewicz

Let f = CAX, then f = sum(i,j)[c_i*a_ij*x_j] and df/da_ij = c_i * x_j. Hence,

df/dA = XC (2x2 matrix)

where, as you wrote, X is a column vector and C is a row vector.

T.J. Moir

A scalar wrt a matrix is easy, the answer is a matrix. ask me again if you have a matrix function wrt a matrix, that is far harder and you get a matrix of matrices.